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ElementMonoidHom functorGrothendieck topologyCategorificationCoequalizerImageNatural transformationClosed categoryEquivalence of categoriesMonadMonoidal functorGroup schemeAllegoryCategory theoryFunctor categoryHom-setExponential objectDirect productClosed monoidal categoryProjective objectRepresentable functorSubcategoryDiagonal morphismSubobject classifierIdentity functorMorphismCategoryInitial and terminal objectsProductCohomologySubobjectFunctorGroupoidMulticategoryToposFull functorQuotient categoryGroup cohomologyString diagramCategory of setsLimitDerived categorySpanProfunctorMonoidal categoryHomological algebraOutline of category theoryDiagramSieveConcrete categoryFormationModel categoryObjectEquivariant cohomologyProduct categorySmall categoryGroup extensionAbelian categoryKernelIdentity morphismCategory of topological spacesF-algebraQuasi-categoryGlobal elementKan extensionGalois connectionHigher category theoryHomotopy theoryGeneral topologyCategory of small categoriesTriangulated categorySimple homotopy theoryAdjoint functorsYoneda embeddingGraph homologyMonomorphismLie algebra extensionKleisli categoryFaithful functorMatroidConeDagger categoryRing homomorphismCoproductCosmosGalois cohomologyHigher-dimensional algebraFull and faithful functorsElementary toposSet theoryUniversal propertyTransfinite inductionHomotopy type theoryRelative homologyMonad transformerConstructible universeCellular homologyAlgebraic data typeCategory of relations